Nonlinear Power Research Articles

Neural modeling of power nonlinear inductors by the E-α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}Net network

In this paper, a model for nonlinear ferrite power inductors based on the α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}Net neural network is proposed. The model is able to reproduce the ferrite power inductors inductor behavior up to saturation, considering the core temperature. The α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}Net neural network was used for its generalization capability considering a hybrid approach encompassing a classical weighted interpolation. The model’s effectiveness was experimentally verified by calculating the current flowing through two inductors in an electric circuit in different operating conditions, and has been compared with the two main models found in literature to show the improvement both in terms of the maximum value of the estimated current and the root mean square error. The modeling procedure can be easily extended to inductors with different sizes and core materials due to the features of the α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}Net network and the hybrid approach to retrieve data.

Weakly Coupled Systems of Semi-Linear Fractional σ–Evolution Equations with Different Power Nonlinearities

Weakly Coupled Systems of Semi-Linear Fractional σ–Evolution Equations with Different Power Nonlinearities

Probabilistic power flow based on physics-guided graph neural networks

Under the high-dimensional and nonlinear stochastic power system environment, artificial intelligence (AI) is becoming a promising alternative to the urgent demand for probabilistic power flow (PPF). However, traditional AI only learns from experiences in data and is unable to satisfy physical constraints. This may result in an undesired infeasible inference for PPF. To solve this issue, a physics-guided graph neural network (PG-GNN)-based PPF analysis method is proposed. At the outset, alternating current power flow equation is analyzed to produce gradients for connecting physical component and AI. The proposed PG-GNN then incorporates the sensitivities into the training tensor graph such that it enables in-depth physical learning. At the same time, the GNN serves to enhance generalizability in varying topology. The well-trained PG-GNN is finally leveraged to surrogate traditional power flow solver in Monte-Carlo method, such that real-time PPF is realized. Numerical tests on benchmarks demonstrate that, in unseen scenarios, the proposed method enables only little gap versus the exact baseline, but beats other rivals with over tenfold computing efficiency. Moreover, comparisons with traditional AIs manifest that our method holds better generalizability.

Dark scattering: accelerated constraints from KiDS-1000 with ReACT and CosmoPower

ABSTRACT We present constraints on the dark scattering model through cosmic shear measurements from the Kilo Degree Survey (KiDS-1000), using an accelerated pipeline with novel emulators produced with CosmoPower. Our main emulator, for the dark scattering non-linear matter power spectrum, is trained on predictions from the halo model reaction framework, previously validated against simulations. Additionally, we include the effects of baryonic feedback from HMCode2016, whose contribution is also emulated. We analyse the complete set of statistics of KiDS-1000, namely band powers, COSEBIs, and correlation functions, for dark scattering in two distinct cases. In the first case, taking into account only KiDS cosmic shear data, we constrain the amplitude of the dark energy–dark matter interaction to be $\vert A_{\rm ds} \vert \lesssim 20$$\rm b\,GeV^{-1}$ at 68 per cent C.L. Furthermore, we add information from the cosmic microwave background (CMB) from Planck, along with baryon acoustic oscillations (BAO) from 6dFGS, SDSS, and BOSS, approximating a combined weak lensing+CMB+BAO analysis. From this combination, we constrain $A_{\rm ds} = 10.6^{+4.5}_{-7.3}$$\rm b\,GeV^{-1}$ at 68 per cent C.L. We confirm that with this estimated value of $A_{\rm ds}$ the interacting model considered in this work offers a promising alternative to solve the $S_8$ tension.

Adaptive Finite-Time Prescribed Performance Control of Nonlinear Power Systems with Symmetry Full-State Constraints

Power system control is commonly based on linear controllers, where linear controllers are designed using a linearized model of the system at a specific operating point. However, when the system’s operating point is changed, the dynamic characteristics of the system shift significantly. At this point, linear controllers often fail to meet system stability requirements. Furthermore, the range of state variables in the power system is limited by the objective conditions. In addition, the power system has high-precision constraints on the deviation of the load frequency and so on. Therefore, it is worth designing a finite-time controller that satisfies the prescribed performance and full-state constraints based on the nonlinear model of the power systems. Firstly, the prescribed performance is incorporated into the barrier Lyapunov function to ensure that the tracking error is within the desired accuracy. Then, the tracking strategy is designed based on backstepping and incorporating a first-order filter to ensure that the controlled system’s signals and tracking errors remain bounded in finite time. Finally, two simulations are given to illustrate the effectiveness of the proposed control scheme, confirming that all states keep within the predefined range.

Efficient resource allocation for IoT applications in mobile edge computing via dynamic request scheduling optimization

This study investigates the challenges of task scheduling and resource allocation in an ultra-dense edge cloud (UDEC) network incorporating micro (macro) base stations and different equipment users (UE) under 5G technology. By utilizing multiple access interference (MAI), we enable multiple access capabilities to the UEs under the Non-Orthogonal Multiple Access (NOMA) protocol. To accommodate the dynamic nature of user tasks, we propose a two-level scheduling framework. At the upper level, the non-convex, non-linear power allocation problem for mobile users is formulated and solved using the Inertia Weight Particle Swarm Optimization (IW-PSO) algorithm to minimize the transmission energy consumption. Simultaneously, at the lower level, the joint task offloading and resource allocation problem is formulated as MINP and solved with the binary Particle Swarm Optimization (PSO) algorithm to find an optimal schedule that maximizes the response rate and the overall welfare of the system while minimizing the energy consumption. In this study, various sensitivity analyses are conducted for different parameters, including the number of mobile users, channel power, and request profile parameters, including workload and request size. Comparative analyses with other methods from recent literature consistently reveal the comparable performance of the proposed framework and confirm its effectiveness in addressing the challenges of dynamic task scheduling.

Design and Development of Fractional Order Convolutional Neural Network Based Fractional Order Nonlinear Reactor Power Simulator for CANDU-PHWR

A highly complex nonlinear Reactor Regulating System (RRS) of Canadian Deuterium Uranium Pressurized Heavy Water Reactor (CANDU-PHWR) based Nuclear Power Plant (NPP) simulated in the present research. The internal design of RRS is secured and vendor controlled which is embedded in AC-132 Programmable Logic Controller (PLC). Therefore, the problem of the identification of the RRS controller model is addressed. A data-driven Fractional Order Nonlinear MIMO Hammerstein Model (FO-NC-MIMO-HM) of NPP is identified using an Adaptive Immune Algorithm (AIA) based on a Global Search Strategy (GSS) and Auxiliary Model Recursive Least Square Method (AMRLSM). Parameters of FO-MIMO-HM are identified using Innovative Real-Time Plant Operational Data (IRTPOD). The original PLC-based controller is replaced with a new Fractional Order Convolutional Neural Network (FO-CNN) based Fractional Order Nonlinear Controller (FO-NC). Therefore, a visual Simulator is developed for detailed modeling, control, simulation, and analysis of the proposed design scheme for RRS in Visual Basic (VB) Software. The performance of the proposed design scheme is tested and validated for different modes of RRS against benchmark data obtained from Plant Data Recorder (PDR) and found in close agreement well within the design bounds.

Can we compute the worst voltage case under power flows uncertainty at TSO-DSO interfaces?

This paper proposes the new problem of calculating the worst-voltage-case (WVC) under power flows uncertainty, particularly at interfaces between transmission and distribution grid operators. The goal of the calculation is to verify if the realization of the worst uncertainty scenario leads to abnormal voltages, or assure where the voltage instability is not a risk, and inform the transmission system operator. The problem is formulated as a tailored non-convex, nonlinear optimal power flow (OPF) with complementarity or equilibrium constraints (ECs). The latter model the generator switch between under voltage control and under reactive power limit. The problem is converted into a mathematically equivalent nonlinear programming OPF problem in which ECs are handled as penalty terms in the objective function. The paper has conducted a series of experiments on the 60-bus Nordic system, which have pointed out the challenges associated to such computations to obtain meaningful results and unveiled new insights. The findings and scalability are confirmed using a real-world 1203-bus system.

Enhanced Kepler Optimization Method for Nonlinear Multi-Dimensional Optimal Power Flow

Enhanced Kepler Optimization Method for Nonlinear Multi-Dimensional Optimal Power Flow

Indicator of abnormal cathode electron emission state with gas flow in Hall thrusters

The accurate diagnosis of abnormal electron emission state in hollow cathodes is crucial for the stable operation of Hall electric propulsion systems. In this study, a method of reducing the cathode working gas flow rate was used to simulate abnormal working conditions in which the cathode electron emission state (CEES) was deteriorating. By analyzing and comparing the oscillation signals under abnormal and steady-state working conditions, it was found that as the CEES deteriorated, the power content of the breathing oscillation decreased in the 1–40 kHz frequency band, and the main frequency decreased; in contrast, the power content of the transit-time oscillation increased in the 100–500 kHz range, and the main frequency was on the rise. Combined with the current growth rate analysis of breathing and transit-time oscillations, when the cathode gas flow rate decreases, the CEES deteriorates, the coupling voltage drop increases, and the potential drop in the channel decreases. The electron temperature and nonlinear power absorption of the electrons decrease, leading to a decrease in the growth rate of breathing oscillations and the breathing oscillation weakens; however, the time-averaged ion velocity and ion sound velocity in the channel decrease simultaneously, but the ion velocity decreases significantly faster than the ion sound velocity, leading to an increase in the growth rate of the transit-time oscillation, and the transit-time oscillation strengthen. Through comparison of the oscillation signals under different working conditions, such as varied anode flow rate, anode voltage, magnetic induction, it was proven to be a unique feature of CEES deteriorates, and can be used as an indicator of CEES deteriorates during the on-orbit operation of the Hall-effect thrusters.

Assorted Spatial Optical Dynamics of a Generalized Fractional Quadruple Nematic Liquid Crystal System in Non-Local Media

Nematicons upgrade the recognition of light localization in the reorientation of non-local media. the current research employs a powerful integral scheme using a different procedure, namely, the modified simple equation method (MSEM), to analyze nematicons in liquid crystals from the controlling model. The expanded MSEM is investigated to enlarge the applicability of the standard one. The suggested expansion depends on merging the MSEM and the ansatz method. The new generalized nonlinear n-times quadruple power law is included. With the aid of the symbolic computational package Mathematica, new explicit complex hyperbolic, periodic, and more exact spatial soliton solutions are derived. Moreover, the related existence constraints are obtained. To show the dynamical properties of some of the obtained nematicons, three-dimensional profiles with corresponding contours are depicted with the choice of appropriate values of arbitrary parameters. The fractional impacts in various applicable senses are analyzed to investigate the generality of the considered model.

When Maturation is Not Linear: Brain Oscillatory Activity in the Process of Aging as Measured by Electrophysiology.

Changes in brain oscillatory activity are commonly used as biomarkers both in cognitive neuroscience and in neuropsychiatric conditions. However, little is known about how its profile changes across maturation. Here we use regression models to characterize magnetoencephalography power changes within classical frequency bands in a sample of 792 healthy participants, covering the range 13 to 80 years old. Our findings unveil complex, non-linear power trajectories that defy the traditional linear paradigm, with notable cortical region variations. Interestingly, slow wave activity increases correlate with improved cognitive performance throughout life and larger gray matter volume in the elderly. Conversely, fast wave activity diminishes in adulthood. Elevated low-frequency activity during aging, traditionally seen as compensatory, may also signify neural deterioration. This dual interpretation, highlighted by our study, reveals the intricate dynamics between brain oscillations, cognitive performance, and aging. It advances our understanding of neurodevelopment and aging by emphasizing the regional specificity and complexity of brain rhythm changes, with implications for cognitive and structural integrity.

Dispatchable region for distributed renewable energy generation in reconfigurable AC–DC distribution networks with soft open points

The dispatchable region (DR) describes the ability of a power system to adapt to the variability of distributed renewable energy (DRE) generation. Switchable devices such as soft open points (SOPs) and tie switches enable the AC–DC distribution network to flexibly cope with DRE power fluctuations. Currently, research on DRs seldom considers the effects of SOPs and reconfiguration with tie switches in AC–DC distribution networks, which prevents accurate evaluation of DR for this type of network. To bridge this gap, this paper formulates DRs for DRE generation in an AC–DC distribution network considering SOPs and reconfiguration with tie switches. The original model for deriving DRs is typically nonconvex, and the DR boundaries are intractable because of nonlinear power flow equations and binary variables of tie switches. Accordingly, this paper employs the outer polyhedral approximation and convex hull relaxation to approximate the original DR. An efficient adaptive constraint generation algorithm is developed to search for boundaries of the approximated DR. The numerical results show that the proposed model can effectively adapt to the DR of reconfigurable AC–DC distribution networks with SOPs and verify the accuracy and computational efficiency of the proposed method.

Exploiting Signal Propagation Delays to Match Task Memory Requirements in Reservoir Computing.

Recurrent neural networks (RNNs) transmit information over time through recurrent connections. In contrast, biological neural networks use many other temporal processing mechanisms. One of these mechanisms is the inter-neuron delays caused by varying axon properties. Recently, this feature was implemented in echo state networks (ESNs), a type of RNN, by assigning spatial locations to neurons and introducing distance-dependent inter-neuron delays. These delays were shown to significantly improve ESN task performance. However, thus far, it is still unclear why distance-based delay networks (DDNs) perform better than ESNs. In this paper, we show that by optimizing inter-node delays, the memory capacity of the network matches the memory requirements of the task. As such, networks concentrate their memory capabilities to the points in the past which contain the most information for the task at hand. Moreover, we show that DDNs have a greater total linear memory capacity, with the same amount of non-linear processing power.

Existence and multiplicity of solutions for fractional p-Laplacian equation involving critical concave-convex nonlinearities

Abstract We investigate the following fractional p-Laplacian convex-concave problem: ( P λ ) ( − Δ ) p s u = λ | u | q − 2 u + | u | p s * − 2 u in Ω , u = 0 in R n \ Ω , $$\left({P}_{\lambda }\right) \begin{cases}\begin{aligned}\hfill {\left(-{\Delta}\right)}_{p}^{s}u& =\lambda \vert u{\vert }^{q-2}u+\vert u{\vert }^{{p}_{s}^{{\ast}}-2}u\hfill & \hfill & \quad \text{in} {\Omega},\hfill \\ \hfill u& =0 \hfill & \hfill & \quad \text{in} {\mathbb{R}}^{n}{\backslash}{\Omega},\hfill \end{aligned}\quad \hfill \end{cases}$$ where Ω is a bounded C 1,1 domain in R n ${\mathbb{R}}^{n}$ , s ∈ (0, 1), p > q > 1, n > sp, λ > 0, and p s * = n p n − s p ${p}_{s}^{{\ast}}=\frac{np}{n-sp}$ is the critical Sobolev exponent. Our analysis extends classical works (A. Ambrosetti, H. Brezis, and G. Cerami, “Combined effects of concave and convex nonlinearities in some elliptic problems,” J. Funct. Anal., vol. 122, no. 2, pp. 519–543, 1994, B. Barrios, E. Colorado, R. Servadei, and F. Soria, “A critical fractional equation with concave-convex power nonlinearities,” Ann. Inst. Henri Poincare Anal. Non Lineaire, vol. 32, no. 4, pp. 875–900, 2015, J. García Azorero, J. Manfredi, and I. Peral Alonso, “Sobolev versus Hölder local minimizer and global multiplicity for some quasilinear elliptic equations,” Commun. Contemp. Math., vol. 2, no. 3, pp. 385–404, 2000) to fractional p-Laplacian. Owing to the nonlinear and nonlocal properties of ( − Δ ) p s ${\left(-{\Delta}\right)}_{p}^{s}$ , we need to overcome many difficulties and apply notably different approaches, due to the lack of Picone identity, the stability theory, and the strong comparison principle. We show first a dichotomy result: a positive W 0 s , p ( Ω ) ${W}_{0}^{s,p}\left({\Omega}\right)$ solution of (P λ ) exists if and only if λ ∈ (0, Λ] with an extremal value Λ ∈ (0, ∞). The W 0 s , p ( Ω ) ${W}_{0}^{s,p}\left({\Omega}\right)$ regularity for the extremal solution seems to be unknown regardless of whether s = 1 or s ∈ (0, 1). When p ≥ 2, p − 1 < q < p and n > s p ( q + 1 ) q + 1 − p $n{ >}\frac{sp\left(q+1\right)}{q+1-p}$ , we get two positive solutions for (P λ ) with small λ > 0. Here the mountain pass structure is more involved than the classical situations due to the lack of explicit minimizers for the Sobolev embedding, we should proceed carefully and simultaneously the construction of mountain pass geometry and the estimate for mountain pass level. Finally, we show another new result for (P λ ) and all p > q > 1: without sign constraint, (P λ ) possesses infinitely many solutions when λ > 0 is small enough. Here we use the Z 2 ${\mathbb{Z}}_{2}$ -genus theory, based on a space decomposition for reflexible and separable Banach spaces, which has its own interest.

Ground states for coupled NLS equations with double power nonlinearities

Ground states for coupled NLS equations with double power nonlinearities

Non-Linear Phenomena in Voltage and Frequency Converters Supplying Non-Thermal Plasma Reactors

Atmospheric pressure cold plasmas have recently been the subject of intense research and applications for solving problems in the fields of energy, environmental engineering, and biomedicine. Non-thermal atmospheric pressure plasma sources, with dielectric barrier discharges, plasma jets, and arc discharges, are non-linear power loads. They require special power systems, which are usually designed separately for each type of plasma reactor, depending on the requirements of the plasma-chemical process, the power of the receiver, the type of process gas, the current, voltage and frequency requirements, and the efficiency of the power source. This paper presents non-linear phenomena accompanying plasma generation in the power supply plasma reactor system, such as harmonic generation, resonance, and ferroresonance of currents and voltages, and the switching of overvoltages and pulse generation. When properly applied, this can support the operation of the above-mentioned reactors by providing improved discharge ignition depending on the working gas, thus increasing the efficiency of the plasma process and improving the cooperation of the plasma-generation system with the power supply.

Enhancing energy efficiency in power looms: utilizing regression machine learning for electrokinetic energy assessment

This study focuses on optimizing electro-kinetic energy utilization in textile weaving units, addressing power interruptions, reducing electrical costs, and harnessing latent kinetic energy during the weaving process. Power looms, vital to textile production, often incur inefficiencies and increased operational costs due to underutilized kinetic energy. To address these challenges, three innovative electrokinetic energy harvesting approaches are proposed: the Modified Series-Parallel Piezo Matrix, bi-directional linear generation, and uni-directional non-linear power extraction methods. The research further incorporates the Super Lift and Ultra Lift DC-DC power conversion techniques to enhance energy efficiency. The Modified Series-Parallel Piezo Array integrates Piezoelectric elements to capture and convert discarded kinetic energy efficiently. The bi-directional linear generation method captures mechanical energy from both forward and backward movements in weaving, minimizing energy wastage. The uni-directional non-linear power extraction method optimizes energy recovery by targeting specific weaving cycle phases. Machine learning algorithms, including Gaussian Process Regression, Linear Regression, Neural Network, and Support Vector Machine, enable precise energy estimation for meticulous modeling and optimization. Rigorous validation through MATLAB simulations aims to bolster energy efficiency, trim operational costs, and promote sustainable energy practices in the textile industry, contributing to a more environmentally friendly and sustainable future for the sector.

SYREN-HALOFIT: A fast, interpretable, high-precision formula for the ΛCDM nonlinear matter power spectrum

Context. Rapid and accurate evaluation of the nonlinear matter power spectrum, P(k), as a function of cosmological parameters and redshift is of fundamental importance in cosmology. Analytic approximations provide an interpretable solution, yet current approximations are neither fast nor accurate relative to numerical emulators. Aims. We aim to accelerate symbolic approximations to P(k) by removing the requirement to perform integrals, instead using short symbolic expressions to compute all variables of interest. We also wish to make such expressions more accurate by re-optimising the parameters of these models (using a larger number of cosmologies and focussing on cosmological parameters of more interest for present-day studies) and providing correction terms. Methods. We use symbolic regression to obtain simple analytic approximations to the nonlinear scale, kσ, the effective spectral index, neff, and the curvature, C, which are required for the HALOFIT model. We then re-optimise the coefficients of HALOFIT to fit a wide range of cosmologies and redshifts. We then again exploit symbolic regression to explore the space of analytic expressions to fit the residuals between P(k) and the optimised predictions of HALOFIT. Our results are designed to match the predictions of EUCLIDEMULATOR2, but we validate our methods against N-body simulations. Results. We find symbolic expressions for kσ, neff and C which have root mean squared fractional errors of 0.8%, 0.2% and 0.3%, respectively, for redshifts below 3 and a wide range of cosmologies. We provide re-optimised HALOFIT parameters, which reduce the root mean squared fractional error (compared to EUCLIDEMULATOR2) from 3% to below 2% for wavenumbers k = 9 × 10−3 − 9 h Mpc−1. We introduce SYREN-HALOFIT (symbolic-regression-enhanced HALOFIT), an extension to HALOFIT containing a short symbolic correction which improves this error to 1%. Our method is 2350 and 3170 times faster than current HALOFIT and HMCODE implementations, respectively, and 2680 and 64 times faster than EUCLIDEMULATOR2 (which requires running CLASS) and the BACCO emulator. We obtain comparable accuracy to EUCLIDEMULATOR2 and the BACCO emulator when tested on N-body simulations. Conclusions. Our work greatly increases the speed and accuracy of symbolic approximations to P(k), making them significantly faster than their numerical counterparts without loss of accuracy.

A novel PQ improvement in multi-parallel feeder distribution system using multi-convertible UPQC device

In the current situation, the use of non-linear power electronic devices in automated industries, arc-furnaces, and adjustable speed drives. The nature of large-sized non-linear loads causes harmonic pollution, voltage interruptions, and voltage sag/swell issues, which are the main issues in modern multi-parallel feeder distribution network. Several mitigation techniques among the above, the multi-convertible universal power-quality conditioner has reliable performance, robust operation and also mitigation of both current-voltage allied power quality (PQ) issues accordingly. The multi-convertible universal power-quality conditioner (Mcon-UPQC) device mitigates power-quality issues by extracting deviated supply voltage and distorted load current by using feasible control algorithm. But, the computational delay, complex mathematical transformation and response delay are the major problem identified in conventional control algorithms. In this work, a novel generalized vector reference control algorithm has been proposed for extraction of fundamental reference voltage-current signals. The performance and effectiveness of proposed control algorithm of Mcon-UPQC device is validated by using MATLAB-Simulink computing tool, simulated outcomes are illustrated with valid comparisons.